Dynamics of a colloidal particle coupled to a Gaussian field: from a confinement-dependent to a non-linear memory

Abstract

The effective dynamics of a colloidal particle immersed in a complex medium is often described in terms of an overdamped linear Langevin equation for its velocity with a memory kernel which determines the effective (time-dependent) friction and the correlations of fluctuations. Recently, it has been shown in experiments and numerical simulations that this memory may depend on the possible optical confinement the particle is subject to, suggesting that this description does not capture faithfully the actual dynamics of the colloid, even at equilibrium. Here, we propose a different approach in which we model the medium as a Gaussian field linearly coupled to the colloid. The resulting effective evolution equation of the colloidal particle features a non-linear memory term which extends previous models and which explains qualitatively the experimental and numerical evidence in the presence of confinement. This non-linear term is related to the correlations of the effective noise via a novel fluctuation-dissipation relation which we derive.

arXiv comment34 pages, 7 figures

References in corpus (16)

• Critical Casimir effect in classical binary liquid mixtures
• Symmetries of generating functionals of Langevin processes with colored multiplicative noise
• Transient dynamics of a colloidal particle driven through a viscoelastic fluid
• Nonequilibrium critical Casimir interactions in binary fluids
• Generalized Langevin equations for a driven tracer in dense soft colloids: construction and applications
• A perturbative path integral study of active and passive tracer diffusion in fluctuating fields
• Fluid viscoelasticity triggers fast transitions of a Brownian particle in a double well optical potential
• Barrier crossing in a viscoelastic bath
• Fluctuations of the Casimir-like force between two membrane inclusions
• Properties of a nonlinear bath: Experiments, theory, and a stochastic Prandtl-Tomlinson model
• Energy transfer between colloids via critical interactions
• Driven probe under harmonic confinement in a colloidal bath
• Drag Coefficient of a Rigid Spherical Particle in a Near-Critical Binary Fluid Mixture beyond the Regime of the Gaussian Model
• Dynamics of a tagged monomer: Effects of elastic pinning and harmonic absorption
• Dynamics and steady states of a tracer particle in a confined critical fluid
• Spatial Organization of Active Particles with Field Mediated Interactions

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